Extremum of second-order directional derivatives

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Abstract

In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.

Keywords

Finite point method second-order directional derivative extremum 

MR Subject Classification

26B05 65D25 
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References

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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.National Key Laboratory of Science and Technology on Computational PhysicsInstitute of Applied Physics and Computational MathematicsBeijingChina

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